Zinc Fermi level

A knowledge of the behavior of d orbitals is essential to understand the differences and trends in reactivity of the transition metals. The width of the d band decreases as the band is filled when going to the right in the periodic table since the molecular orbitals become ever more localized and the overlap decreases. Eventually, as in copper, the d band is completely filled, lying just below the Fermi level, while in zinc it lowers further in energy and becomes a so-called core level, localized on the individual atoms. If we look down through the transition metal series 3d, 4d, and 5d we see that the d band broadens since the orbitals get ever larger and therefore the overlap increases. 

Mandal KC (1990) Fermi level shift with photovoltages at zinc modified CdSe surfaces. J Mater Sci Lett 9 1203-1204... 

Fig. 1.13. Top Variation of defect formation enthalpies with Fermi level under zinc- (left) and oxygen-rich (right) conditions as obtained from GGA+U calculations. The gray shaded area indicates the difference between the calculated and the experimental band gap. The numbers in the plot indicate the defect charge state parallel lines imply equal charge states Bottom Transition levels in the band gap calculated within GGA (a), GGA+U (b) and using an extrapolation formula described in [115]. The dark gray shaded areas indicate error bars. Copyright (2006) by the American Physical Society...

Erhart and Albe also calculated zinc diffusion in ZnO [130]. The results are displayed in Fig. 1.18 together with a comparison to experimental data. Depending on chemical potential and Fermi level position either zinc vacancy or zinc interstitial diffusion can dominate. In the case of n-type material, where the Fermi level is close to the conduction band, zinc diffusion is mostly accomplished via the vacancy mechanism. 

Fig. 1.18. Zinc diffusion in ZnO [130]. Top Dependence of diffusivity on chemical potential and Fermi level at a temperature of 1 300 K illustrating the competition between vacancy and interstitial mechanisms. The shaded grey areas indicate the ranges selected for comparison with experimental data. Bottom Comparison between calculation and experiment. Experimental data from Lindner [137], Secco and Moore [138,139], Moore and Williams [131], Wuensch and Tuller [143], Tomlins et al. [62], and Nogueira et al. [144,145]. Solid and dashed lines correspond to regions I (vacancy mechanism) and II (interstitial(cy) mechanism) in the top graph, respectively. Reprinted with permission from [130]. Copyright (2006), American Institute of Physics...

In 1948 Verwey and his co-workers (88) established that lithium ions incorporated into nickel oxide produced an equivalent number of Ni + ions and so enhanced the electrical conductivity. Later, from measurements of the Seebeck effect, Parravano (89) confirmed that in the presence of lithium the Fermi level of nickel oxide is indeed depressed in accordance with the increased concentration of positive holes. For trivalent additions, Hauffe and Block (90) have shown that the incorporation of small amounts of Cr + ions decreases the conductivity of nickel oxide one infers accordingly that the hole concentration is decreased and that the Fermi level is raised. This is therefore an attractive situation with which to examine the influence of the height of the Fermi level on catalytic activity. The most appropriate n-type oxide for analogous studies is zinc oxide. 

We normally define the energy level of electrons in a solid in terms of the Fermi level, eF, which is essentially equivalent to the electrochemical potential of electrons in the solid. In the case of metals, the Fermi level is equal to the highest occupied level of electrons in the partially filled frontier band. In the case of semiconductors of covalent and ionic solids, by contrast, the Fermi level is situated within the band gap where no electron levels are available except for localized ones. A semiconductor is either n-type or p-type, depending on its impurities and lattice defects. For n-type semiconductors, the Fermi level is located close to the conduction band edge, while it is located close to the valence band edge for p-type semiconductors. For examples, a zinc oxide containing indium as donor impurities is an n-type semiconductor, and a nickel oxide containing nickel ion vacancies, which accept electrons, makes a p-type semiconductor. In semiconductors, impurities and lattice defects that donate electrons introduce freely mobile electrons in the conduction band, and those that accept electrons leave mobile holes (electron vacancies) in the valence band. Both the conduction band electrons and the valence band holes contribute to electronic conduction in semiconductors. 

Fig. 3. Illustrations of (a) the geometrical arrangement of zinc and oxygen species on the ZnO(lOlO) non-polar surface, and (b) the electronic energy levels adjacent to the surface. Evac, Ec, Ef, and Ev denote, respectively, the energy level of electrons in vacuum, at the bottom of the bulk conduction band, at the Fermi level, or at the top of the valence band. Discrete energy levels associated with oxygen or zinc vacancies are denoted by Ey0 anc respectively. Bands of surface states associated with...

M. B. Panish and H. C. Casey, Jr., The 1040° solid solubility isotherm of zinc in GaP the Fermi level as a function of hole concentration, J. Phys. Chem. Solids 28 (1968) 1719-1726. 

Figure 16. Triboelectric charging of substituted polystyrene films vs. (lP+EA)/2 to estimate Fermi level of zinc.

Figure3.17 Calculated defectformation energies for main native point defects in ZnO as a function of the Fermi level under (a) zinc-rich conditions and (b) oxygen-rich conditions. Only the segments corresponding to the lowest formation energy values are shown. The zero of the Fermi level is set to the top of the valence band. Kinks for each defect indicate transitions between different charge states (0, —1, —2). (After Ref [88].)...

A theoretical interpretation relating the valence electron concentration and the structure was put forward by H. Jones. If we start from copper and add more and more zinc, the valence electron concentration increases. The added electrons have to occupy higher energy levels, i.e. the energy of the Fermi limit is raised and comes closer to the limits of the first Brillouin zone. This is approached at about VEC = 1.36. Higher values of the VEC require the occupation of antibonding states now the body-centered cubic lattice becomes more favorable as it allows a higher VEC within the first Brillouin zone, up to approximately VEC = 1.48. 

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